606 research outputs found
Duality Principle and Braided Geometry
We give an overview of a new kind symmetry in physics which exists between
observables and states and which is made possible by the language of Hopf
algebras and quantum geometry. It has been proposed by the author as a feature
of Planck scale physics. More recent work includes corresponding results at the
semiclassical level of Poisson-Lie groups and at the level of braided groups
and braided geometry.Comment: 24 page
Projective quantum spaces
Associated to the standard R-matrices, we introduce quantum
spheres , projective quantum spaces , and quantum
Grassmann manifolds . These algebras are shown to be
homogeneous quantum spaces of standard quantum groups and are also quantum
principle bundles in the sense of T Brzezinski and S. Majid (Comm. Math. Phys.
157,591 (1993)).Comment: 8 page
Braided Hopf Algebras and Differential Calculus
We show that the algebra of the bicovariant differential calculus on a
quantum group can be understood as a projection of the cross product between a
braided Hopf algebra and the quantum double of the quantum group. The resulting
super-Hopf algebra can be reproduced by extending the exterior derivative to
tensor products.Comment: 8 page
Comment on "Fermionic entanglement ambiguity in noninertial frames"
In this comment we show that the ambiguity of entropic quantities calculated
in Physical Review A 83, 062323 (2011) for fermionic fields in the context of
Unruh effect is not related to the properties of anticommuting fields, as
claimed in Physical Review A 83, 062323 (2011), but rather to wrong
mathematical manipulations with them and not taking into account a fundamental
superselection rule of quantum field theory.Comment: To appear in Physical Review A. Some of the problems discussed in
this comment can also be found in other previously published papers studying
the Unruh effect for fermions (in the context of quantum information theory).
An extended version of the comment can be found here
http://arxiv.org/abs/1108.555
Deformed Minkowski spaces: clasification and properties
Using general but simple covariance arguments, we classify the `quantum'
Minkowski spaces for dimensionless deformation parameters. This requires a
previous analysis of the associated Lorentz groups, which reproduces a previous
classification by Woronowicz and Zakrzewski. As a consequence of the unified
analysis presented, we give the commutation properties, the deformed (and
central) length element and the metric tensor for the different spacetime
algebras.Comment: Some comments/misprints have been added/corrected, to appear in
Journal of Physics A (1996
Coadditive differential complexes on quantum groups and quantum spaces
A regular way to define an additive coproduct (or ``coaddition'') on the
q-deformed differential complexes is proposed for quantum groups and quantum
spaces related to the Hecke-type R-matrices. Several examples of braided
coadditive differential bialgebras (Hopf algebras) are presented.Comment: 9 page
Examples of q-regularization
An Introduction to Hopf algebras as a tool for the regularization of relavent
quantities in quantum field theory is given. We deform algebraic spaces by
introducing q as a regulator of a non-commutative and non-cocommutative Hopf
algebra. Relevant quantities are finite provided q\neq 1 and diverge in the
limit q\rightarrow 1. We discuss q-regularization on different q-deformed
spaces for \lambda\phi^4 theory as example to illustrate the idea.Comment: 17 pages, LaTex, to be published in IJTP 1995.1
Solutions of Klein--Gordon and Dirac equations on quantum Minkowski spaces
Covariant differential calculi and exterior algebras on quantum homogeneous
spaces endowed with the action of inhomogeneous quantum groups are classified.
In the case of quantum Minkowski spaces they have the same dimensions as in the
classical case. Formal solutions of the corresponding Klein--Gordon and Dirac
equations are found. The Fock space construction is sketched.Comment: 21 pages, LaTeX file, minor change
Unbraiding the braided tensor product
We show that the braided tensor product algebra
of two module algebras of a quasitriangular Hopf algebra is
equal to the ordinary tensor product algebra of with a subalgebra of
isomorphic to , provided there exists a
realization of within . In other words, under this assumption we
construct a transformation of generators which `decouples' (i.e.
makes them commuting). We apply the theorem to the braided tensor product
algebras of two or more quantum group covariant quantum spaces, deformed
Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page
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